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Mathematical Model for Diabetes Mellitus with Impulsive Injections of Glucose-insulin WANG Xia, ZHANG Ying, SONG Xin-yu Chinese Quarterly Journal of Mathematics    2017, 32 (2): 118-133.   DOI: 10.13371/j.cnki.chin.q.j.m.2017.02.002 Abstract （139）      PDF（pc） （1111KB）（239）       Knowledge map    Save Impulsive injections of glucose and insulin analogues are very important strategies for the control of diabetes mellitus. We mainly imitate diabetes patients take insulin before eating, and eating approximately as a pulse blood glucose injection, as a result, a new mathematical model with impulsive injections of both glucose and insulin at different fixed times is formulated in this paper. Using the discrete dynamical system determined by the stroboscopic map, we show that the existence and uniqueness of a positive globally asymptotically stable periodic solution for type I diabetes. By impulsive comparison theorem, we obtain the glucose concentration level of the system is uniformly bounded above and below for type Ⅱ diabetes. Numerical analysis verifies our theoretical results.  Related Articles | Metrics

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Well-posedness for A Plat Equations with Nonlocal Source Term LIU Gong-wei, ZHAO Rui-min, ZHANG Hong-wei Chinese Quarterly Journal of Mathematics    2019, 34 (4): 331-342.   DOI: 10.13371/j.cnki.chin.q.j.m.2019.04.001 Abstract （105）      PDF（pc） （757KB）（137）       Knowledge map    Save In this paper,we investigate the initial boundary value problem for a plate equation with nonlocal source term.The local,global existence and exponential decay result are established under certain conditions.Moreover,we also prove the blow-up in finite time and the lifespan of solution under certain conditions.  Related Articles | Metrics

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Asymptotic Property of Solutions in a 4th-Order Parabolic Model for Epitaxial Growth of Thin Film#br# SUN An-qi, LI Feng-jie Chinese Quarterly Journal of Mathematics    2022, 37 (2): 162-177.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.006 Abstract （79）      PDF（pc） （421KB）（56）       Knowledge map    Save This paper deals with a homogeneous Neumann initial-boundary problem of a 4th-order parabolic equation modeling epitaxial growth of thin film. We determine the classification of initial energy on the existence of blow-up, global existence and extinction of solutions by using the potential well method and the auxiliary function method. Moreover, asymptotic estimates on global solution and extinction solution are studied, respectively. Related Articles | Metrics

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Italian Domination of Strong Product of Two Paths WEI Li-yang, LI Feng Chinese Quarterly Journal of Mathematics    2024, 39 (3): 221-234.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.001 Abstract （26）      PDF（pc） （392KB）（19）       Knowledge map    Save The domination problem of graphs is an important issue in the field of graph theory. This paper mainly considers the Italian domination number of the strong product between two paths. By constructing recursive Italian dominating functions, the upper bound of its Italian domination number is obtained, and then a partition method is proposed to prove its lower bound. Finally, this paper yields a sharp bound for the Italian domination number of the strong product of paths. Related Articles | Metrics

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Factorized Smith Method for A Class of High-Ranked Large-Scale T-Stein Equations LI Xiang, YU Bo, TANG Qiong Chinese Quarterly Journal of Mathematics    2024, 39 (3): 235-249.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.002 Abstract （15）      PDF（pc） （11638KB）（13）       Knowledge map    Save We introduce a factorized Smith method (FSM) for solving large-scale highranked J-Stein equations within the banded-plus-low-rank structure framework. To effectively reduce both computational complexity and storage requirements, we develop techniques including deflation and shift, partial truncation and compression, as well as redesign the residual computation and termination condition. Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time. Related Articles | Metrics

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On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems ZHANG Wen-wen, LI Ping-run Chinese Quarterly Journal of Mathematics    2024, 39 (3): 262-269.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.004 Abstract （29）      PDF（pc） （321KB）（17）       Knowledge map    Save This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains. Related Articles | Metrics

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Pseudo S-Asymptotically (ω,c)-Periodic Solutions to Fractional Differential Equations of Sobolev Type MAO Hang-ning, CHANG Yong-kui Chinese Quarterly Journal of Mathematics    2024, 39 (3): 295-306.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.007 Abstract （24）      PDF（pc） （402KB）（9）       Knowledge map    Save In this paper, we firstly recall some basic results on pseudo S-asymptotically (ω,c)-periodic functions and Sobolev type fractional differential equation. We secondly investigate some existence of pseudo S-asymptotically (ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type. We finally present a simple example. Related Articles | Metrics

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Updating Mass and Stiffness Matrices Using Eigenstructure Assignment Methods LIU Li-na, YUAN Yu-ying, YUAN Yong-xin Chinese Quarterly Journal of Mathematics    2021, 36 (4): 419-429.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.04.009 Abstract （74）      PDF（pc） （285KB）（99）       Knowledge map    Save A novel numerical method is presented to update mass and stiffness matrices simultaneously with measured vibration data by means of the combined acceleration and displacement output feedback. By the method, the required displacement and acceleration output feedback gain matrices are determined, and thus the optimal approximation mass matrix and stiffness matrix which satisfy the required orthogonality relation and eigenvalue equation are found. The proposed method is computationally efficient and the updated mass and stiffness matrices are also symmetric and have the compact expressions. The numerical example shows that the proposed method is reliable and attractive. Related Articles | Metrics

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Majority Coloring of r-Regular Digraph XIA Wei-hao, SHI Mei, XIAO Ming-yue, CAI Jian-sheng, WANG Ji-hui Chinese Quarterly Journal of Mathematics    2022, 37 (2): 142-146.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.004 Abstract （218）      PDF（pc） （330KB）（357）       Knowledge map    Save  A majority k-coloring of a digraph D with k colors is an assignment c: V ( D ) →{ 1,2,···,k} , such that for every v∈V (D), we have c(w)=c(v) for at most half of all out-neighbors w∈N+( v ). For a natural number k≥2, a 1/k-majority coloring of a digraph is a coloring of the vertices such that each vertex receives the same color as at most a 1/k proportion of its out-neighbours. Kreutzer, Oum, Seymour, van der Zypen and Wood proved that every digraph has a majority 4-coloring and conjectured that every digraph admits a majority 3-coloring. Gir$\widetilde{a}$o, Kittipassorn and Popielarz proved that every digraph has a 1/k-majority 2k-coloring and conjectured that every digraph admits a 1\k-majority (2k−1)-coloring. We showed that every r -regular digraph D with r>36ln(2n) has a majority 3-coloring and proved that every digraph D with minimum outdegree $\delta^+>\frac{2k^2(2k-1)^2}{(k-1)^2}\ln{[(2k-1)n]}$ has a 1/k-majority (2k−1)-coloring. And we also proved that every r-regular digraph D with  $r>\frac{3k^2(2k-1)}{(k-1)^2} \ln(2n)$ has a 1/k-majority (2k−1)-coloring. Related Articles | Metrics

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Adaptive Image Zooming Algorithm Combining Total Variation Minimization and a Second-order Functional WANG Yan-yan, GAO Ran, GU Cong Chinese Quarterly Journal of Mathematics    2016, 31 (4): 435-440.   DOI: 10.13371/j.cnki.chin.q.j.m.2016.04.013 Abstract （90）      PDF（pc） （588KB）（115）       Knowledge map    Save An image zooming algorithm by using partial differential equations（PDEs） is proposed here. It combines the second-order PDE with a fourth-order PDE. The combined algorithm is able to preserve edges and at the same time avoid the blurry effect in smooth regions. An adaptive function is used to combine the two PDEs. Numerical experiments illustrate advantages of the proposed model.  Related Articles | Metrics

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Some Applications of Surface Curvatures in Theoretical Physics YANG Yi-song Chinese Quarterly Journal of Mathematics    2023, 38 (3): 221-253.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.001 Abstract （240）      PDF（pc） （496KB）（104）       Knowledge map    Save In this survey article, we present two applications of surface curvatures in theoretical physics. The first application arises from biophysics in the study of the shape of cell vesicles involving the minimization of a mean curvature type energy called the Helfrich bending energy. In this formalism, the equilibrium shape of a cell vesicle may present itself in a rich variety of geometric and topological characteristics. We first show that there is an obstruction, arising from the spontaneous curvature, to the existence of a minimizer of the Helfrich energy over the set of embedded ring tori. We then propose a scale-invariant anisotropic bending energy, which extends the Canham energy, and show that it possesses a unique toroidal energy minimizer, up to rescaling, in all parameter regime. Furthermore, we establish some genus-dependent topological lower and upper bounds, which are known to be lacking with the Helfrich energy, for the proposed energy. We also present the shape equation in our context, which extends the Helfrich shape equation. The second application arises from astrophysics in the search for a mechanism for matter accretion in the early universe in the context of cosmic strings. In this formalism, gravitation may simply be stored over a two-surface so that the Einstein tensor is given in terms of the Gauss curvature of the surface which relates itself directly to the Hamiltonian energy density of the matter sector. This setting provides a lucid exhibition of the interplay of the underlying geometry, matter energy, and topological characterization of the system. In both areas of applications, we encounter highly challenging nonlinear partial differential equation problems. We demonstrate that studies on these equations help us to gain understanding of the theoretical physics problems considered. Related Articles | Metrics

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Harvesting in a Toxic Predator-Prey Model with Carrying Capacity and Maturation Double Delays ZHONG Ying, WEI Yu-ming Chinese Quarterly Journal of Mathematics    2023, 38 (4): 331-348.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.001 Abstract （112）      PDF（pc） （589KB）（76）       Knowledge map    Save  In this paper, a model of predator-prey with dual delay in maturation and carrying capacity is discussed, in which the past activity of the prey should have an impact on the carrying capacity, the mature prey initiates defense mechanisms to release toxins when subjected to predation, and a commercial harvest of the prey is performed. The stability of the equilibrium of the system in the absence of delay is examined and the optimal harvesting strategy of the model is proven. By investigating the roots of the characteristic equation and applying normalized theory, the properties of the coexistence equilibrium of the system and the conditions for the occurrence of the Hopf bifurcation in the neighborhood of the positive equilibrium are described for various combinations of delays. In the end, numerical simulations are used to verify theoretical analysis results. Related Articles | Metrics

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Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential LI Nan, ZHAO Hui-yan, XU Li-ping Chinese Quarterly Journal of Mathematics    2024, 39 (3): 250-261.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.003 Abstract （21）      PDF（pc） （425KB）（9）       Knowledge map    Save  In this paper, we mainly focus on the following Choquard equation...... Related Articles | Metrics

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The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms WANG Ji-nan, SUN Da-wei Chinese Quarterly Journal of Mathematics    2024, 39 (3): 315-323.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.009 Abstract （18）      PDF（pc） （314KB）（7）       Knowledge map    Save We study the existence of solutions for Kirchhoff-type equations. Firstly, we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum. Then, we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation when λ is small enough. Related Articles | Metrics

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General Energy Decay of Solutions for A Wave Equation with Nonlocal Nonlinear Damping and Source Terms ZHANG Hong-wei, LI Dong-hao, HU Qing-ying Chinese Quarterly Journal of Mathematics    2020, 35 (3): 302-310.   DOI: 10.13371/j.cnki.chin.q.j.m.2020.03.005 Abstract （169）      PDF（pc） （473KB）（353）       Knowledge map    Save We consider a wave equation with nonlocal nonlinear damping and source terms. We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique. The main difficult is how to handle with the nonlocal nonlinear damping term. Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso（Evolution Equation and Control Theory, 2017（6）:437-470） and Narciso（Evolution Equations and Control Theory, 2020, 9（2）: 487-508）. Related Articles | Metrics

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Cyclic Codes over F2 + uF2 + vF2 LIU Xiu-sheng, LIU Hua-lu Chinese Quarterly Journal of Mathematics    2014, 29 (2): 189-194.   DOI: 10.13371/j.cnki.chin.q.j.m.2014.02.005 Abstract （56）      PDF（pc） （295KB）（150）       Knowledge map    Save We study the structure of cyclic codes of an arbitrary length n over the ring F2+ uF2+ vF2, which is not a finite chain ring. We prove that the Gray image of a cyclic code length n over F2+ uF2+ vF2 is a 3-quasi-cyclic code length 3n over F2.  Related Articles | Metrics

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A Cubic Systen Which Generates Bargmann Poteutial and N-gap Potential CAO Ce-wen Chinese Quarterly Journal of Mathematics    1988, 3 (1): 90-96.   Abstract （65）      PDF（pc） （335KB）（209）       Knowledge map    Save Related Articles | Metrics

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A Posterior Estimates in the Finite Element Methods E Wei-nan, MU Mo, HUANG Hong-ci Chinese Quarterly Journal of Mathematics    1988, 3 (1): 97-107.   Abstract （715）      PDF（pc） （588KB）（381）       Knowledge map    Save Related Articles | Metrics

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Nested Alternating Direction Method of Multipliers to Low-Rank and Sparse-Column Matrices Recovery SHEN Nan , JIN Zheng-fen , WANG Qiu-yu Chinese Quarterly Journal of Mathematics    2021, 36 (1): 90-110.   DOI: 10.13371/j.cnki.chin.q.j.m.2021.01.007 Abstract （367）      PDF（pc） （427KB）（401）       Knowledge map    Save The task of dividing corrupted-data into their respective subspaces can be well illustrated, both theoretically and numerically, by recovering low-rank and sparse-column components of a given matrix. Generally, it can be characterized as a matrix and a `2,1-norm involved convex minimization problem. However, solving the resulting problem is full of challenges due to the non-smoothness of the objective function. One of the earliest solvers is an 3-block alternating direction method of multipliers (ADMM) which updates each variable in a Gauss-Seidel manner. In this paper, we present three variants of ADMM for the 3-block separable minimization problem. More preciously, whenever one variable is derived, the resulting problems can be regarded as a convex minimization with 2 blocks, and can be solved immediately using the standard ADMM. If the inner iteration loops only once, the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner. If the solution from the inner iteration is assumed to be exact, the convergence can be deduced easily in the literature. The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive. Related Articles | Metrics

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EEG Feature Learning Model Based on Intrinsic Time-Scale Decomposition and Adaptive Huber Loss YANG Li-jun, JIANG Shu-yue, WEI Xiao-ge , XIAO Yun-hai Chinese Quarterly Journal of Mathematics    2022, 37 (3): 281-300.   DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.006 Abstract （142）      PDF（pc） （538KB）（368）       Knowledge map    Save According to the World Health Organization, about 50 million people world- wide suffer from epilepsy. The detection and treatment of epilepsy face great challenges. Electroencephalogram (EEG) is a significant research object widely used in diagnosis and treatment of epilepsy. In this paper, an adaptive feature learning model for EEG signals is proposed, which combines Huber loss function with adaptive weight penalty term. Firstly, each EEG signal is decomposed by intrinsic time-scale decomposition. Secondly, the statistical index values are calculated from the instantaneous amplitude and frequency of every component and fed into the proposed model. Finally, the discriminative features learned by the proposed model are used to detect seizures. Our main innovation is to consider a highly flexible penalization based on Huber loss function, which can set different weights according to the influence of different features on epilepsy detection. Besides, the new model can be solved by proximal alternating direction multiplier method, which can effectively ensure the convergence of the algorithm. The performance of the proposed method is evaluated on three public EEG datasets provided by the Bonn University, Childrens Hospital Boston-Massachusetts Institute of Technology, and Neurological and Sleep Center at Hauz Khas, New Delhi(New Delhi Epilepsy data). The recognition accuracy on these two datasets is 98% and 99.05%, respectively, indicating the application value of the new model. Related Articles | Metrics